“Love at first sight? Let me just put on my glasses.” Ljupka Cvetanova, The New Land

When I’m working on the sound design for a new pair of (over-ear, closed) headphones, I have to take off my glasses (which makes it difficult for me to see my computer screen…) I’ll explain.

Let’s over-simplify and consider a block diagram of a closed (and therefore “over-ear”) headphone, sitting on one side of your head. This is represented by Figure 1.

Fig 1. A simplified diagram of an over-ear headphone with a sealed cabinet, sitting correctly on the side of your head.

One of the important things to note there is that the air in the chamber between the headphone diaphragm and the ear canal is sealed from the outside world.

So, if I put such a headphone on an artificial ear (which is a microphone in a small hole in the middle of a plate – it is remarkably well-represented by the red lines in Figure 1….) I can measure its magnitude response. I’ll call this the “reference”. It doesn’t matter to me what the measurement looks like, since this is just a magnitude response which is the combination of the headphone’s response and the artificial ear’s response – with some incorrect positioning thrown into the mix.

Fig 2. The headphones in question, placed on an Artificial Ear for the first measurement.

If I then remove the headphones from the plate, and put them back on, in what I think is the same position, and then do the measurement again, I’ll get another curve.

Then, I’ll subtract the “reference measurement” (the first one) from the second measurement to see what the difference is. An example of this is plotted in Figure 2.

Fig 3. The difference between a magnitude response measurement and the reference measurement of the same ear cup on the same headphones, 1/6th octave smoothed. As you can see, it’s slightly different – but not much. I was VERY careful about re-positioning the headphones on the plate.

Now, let’s consider what happens when the seal is broken. I’ll stick a small piece of metal (actually an Allan key, or a hex wrench, depending on where you live) in between the headphones and the plate, causing a leak in the air between the internal cavity and the outside world, as shown in Figure 4.

Fig 4. A small piece of metal that lifts the leather of the ear cup and causes a small leak around it.

Fig 5. A simplified diagram of an over-ear headphone with a sealed cabinet, sitting incorrectly on the side of your head.

We then repeat the measurement, and subtract the original Reference measurement to see what happened. This is shown in Figure 6.

Fig 6. The magnitude response difference caused by a small leak in the chamber.

As you can see, the leak in the system causes us to lose bass, primarily. In the very low end, the loss is significant – more than 10 dB down at 20 Hz! Basically, what we’ve done here is to create an acoustical high-pass filter. (I’m not going to go into the physics of why this happens… That’s too much information for this posting.) You can also see that there’s a bump around 200 Hz which is also a result of the leak. The sharp peak up at 8 kHz is not caused by the leak – it’s just an artefact of the headphones having moved a little on the plate when I put in the Allen Key.

Now let’s make the leak bigger. I’ll stick the arm of my glasses in between the plate and the leather pad.

Fig 7. The arm of my glasses, stuck in the system to make the leak worse…

The result of this measurement (again with the Reference subtracted) is shown in Figure 8.

Fig 8. The magnitude response difference caused by a bigger leak in the chamber.

Now you can see that the high pass filter’s cutoff frequency has risen, and the resonance in the system has not only increased in frequency (to 400 Hz or so) but also in magnitude (to almost +10 dB! Again, the sharp wiggles at the top are mostly just artefacts caused by changes in position…

Just to check and see that I haven’t done something stupid, I’ll remove the glasses, and run the measurement again…

Fig 9. Back to the original – just as a sanity check

The result of this measurement is shown in Figure 10.

Fig 10. Back to a system without leaks… and a magnitude response that closely matches the original – at least in the low end…

So, there are a couple of things to be learned here…

Firstly, if you and a friend both listen to the same pair of closed, sealed headphones, and you disagree about the relative level of bass, check that you’re both not wearing glasses or large earrings…

The more general interpretation of that previous point is that small leaks in the system have a big effect on the response of the headphones in the low-frequency region. Those leaks can happen as a result of many things – not just the arm of your glasses. Hair can also cause the problem. Or, for example, if the headphones are slightly big, and/or your head is slightly small, then the area where your jaw meets your neck under your pinna (around your mastoid gland) is one possile place for leaks. This can also happen if you have a very sharp corner around your jaw (say you are Audrey Hepburn, for example), and the ear cup padding is stiff. Interestingly, as time passes, the foam and covering soften and may change shape slightly to seal these leaks. So, as the headphones match the shape of your head over time, you might get a better seal and a change in the bass level. This might be interpreted by some people as having “broken in” the headphones – but what you’ve actually done is to “break in” the padding so that it fits your head better.

Secondly, those big, sharp spikes up the high end aren’t insignificant… They’re the result of small movements in the headphones on the measuring system. A similar thing happens when you move headphones on your head – but it can be even more significant due to effects caused by your pinna. This is why, many people, when doing headphone measurements, will do many measurements (say, 5 to 10) and average the results. Those errors in placement are not just the result of shifts on the plate – they may also be caused by differences in “clamping pressure” – so, if I angled the headphones a little on that table, then they might be pressing harder on the artificial ear, possibly only on one side of the ear cup, and this will also change the measured response in the high frequency bands.

Fig 11. My glasses on a B&K HATS used for measurements instead of the artificial ear. Check out that leak… This is similar to the problem that I have when I wear glasses when listening to the same headphones.

Of course, it’s possible to reduce this problem by making the foam more compliant (a fancy word for “squishy”) – which may, in turn, mean that the response will be more different for different users due to different head widths. Or the problem could be reduced by increasing the clamping force, which will in turn make the headphones uncomfortable because they’re squeezing your head. Or, you could embrace the leak, and make a pair of open headphones – but those will not give you much passive noise isolation from the outside world. In fact, you won’t have any at all…

So as you can see, as a manufacturer, this issue has to be balanced with other issues when designing the headphones in the first place…

Or you can just take off your glasses, close your eyes, and listen…

Addendum

Please don’t jump too far in your conclusions as a result of seeing these measurements. You should NOT interpret them to mean that, if you wear glasses, you will get a 10 dB bump at 400 Hz. The actual response that you will get from your headphones depends on the size of the leak, the volume of the chamber in the ear cup (which is partly dependent on the size of your pinna, since that occupies a significant portion of the volume inside the chamber) and other factors.

The take-home message here is: when you’re evaluating a pair of closed, over-ear headphones: small leaks have an effect on the low frequency response, and small changes in position have an effect on the high-frequency response. The details of those effects are almost impossible to predict accurately.